An important feature of the two-layer shallow flow model is that the resulting system of equations cannot be expressed in conservation-law form. Here, the HLLS and ARoe solvers, derived initially for systems of conservation laws, are reformulated and applied to the two-layer shallow flows in a great variety of problems. Their resulting extension and combination allows us to overcome the loss of the hyperbolic character, ensuring energy or exactly balanced property, guarantees positivity of the solution, and provides a correct drying/wetting advance front without requiring tuning parameters. As a result, in those cases where the rich description of internal and external waves cannot be provided by the ARoe solver, HLLS is applied. Variable density is considered in each layer as a result of a bulk density driven by the mixture of different constituents. A wide variety of test cases is presented confirming the properties of this combination, including exactly balanced scenarios in subcritical and subcritical-transcritical scenarios, dam-break problems over bed variations and wet/dry fronts, non-hyperbolic conditions, transcritical exchange flow with loss of hyperbolicity. Despite the complexity of the test cases presented here, accurate and stable simulations are guaranteed, ensuring positivity of the solution without decreasing the time step.

两层浅流模型的一个重要特征是，所得方程组无法以守恒律形式表示。在这里，HLLS和ARoe求解器最初是为守恒定律的系统而派生的，它们被重新构造并应用于存在各种问题的两层浅层流中。它们产生的扩展和组合使我们能够克服双曲线特性的损失，确保能量或精确平衡的性能，保证溶液的正性，并提供正确的干燥/润湿提前量，而无需调整参数。结果，在ARoe求解器无法提供内部和外部波的丰富描述的情况下，将应用HLLS。由于由不同成分的混合物驱动的堆积密度，因此每层都被认为具有可变的密度。提出了各种各样的测试案例，以确认这种组合的特性，包括在亚临界和亚临界-跨临界情况下的精确平衡方案，床层变化和湿/干前沿的溃坝问题，非双曲线条件，跨临界交换流量（损失）双曲线。尽管这里介绍的测试用例很复杂，但仍可以保证准确而稳定的仿真，从而确保解决方案的积极性而不会减少时间步长。坝床变化和湿/干锋面，非双曲线条件，跨临界交换流以及双曲线损失等方面的溃坝问题。尽管这里介绍的测试用例很复杂，但仍可以保证准确而稳定的仿真，从而确保解决方案的积极性而不会减少时间步长。坝床变化和湿/干锋面，非双曲线条件，跨临界交换流以及双曲线损失等方面的溃坝问题。尽管这里介绍的测试用例很复杂，但仍可以保证准确而稳定的仿真，从而确保解决方案的积极性而不会减少时间步长。